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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24720 |
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| _version_ | 1866914227972734976 |
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| author | Li, Ch. Orlov, A. Yu. |
| author_facet | Li, Ch. Orlov, A. Yu. |
| contents | We consider products of $n$ random Hermitian matrices which generalize the one-matrix model and show its relation to Hurwitz numbers which count ramified coverings of certain type. Namely, these Hurwitz numbers count $2k$-fold ramified coverings of the Riemann sphere with arbitrary ramification type over $0$ and $\infty$ and ramifications related to the partition $(2^k)$ (``brickworks'' - involution without fixed points) elsewhere. Products of normal random matrices are also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Products of random Hermitian matrices and brickwork Hurwitz numbers. Products of normal matrices Li, Ch. Orlov, A. Yu. Mathematical Physics We consider products of $n$ random Hermitian matrices which generalize the one-matrix model and show its relation to Hurwitz numbers which count ramified coverings of certain type. Namely, these Hurwitz numbers count $2k$-fold ramified coverings of the Riemann sphere with arbitrary ramification type over $0$ and $\infty$ and ramifications related to the partition $(2^k)$ (``brickworks'' - involution without fixed points) elsewhere. Products of normal random matrices are also considered. |
| title | Products of random Hermitian matrices and brickwork Hurwitz numbers. Products of normal matrices |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2512.24720 |